The pressure ( P ) and temperature ( T ) relationship of an ideal gas obeys the equation P T 2 = constant. The volume expansion coefficient of the gas will be :

Step-by-step solution

Given here, P T 2 = constant . . . 1 Using ideal gas equation, P V = n R T We have, P = n R T V Putting in equation 1 , P T 2 = n R T V × T 2 = constant ⇒ T 3 = K V       . . . 2 Differentiating the equation with respect to T , So, d d T K V = 3 T 2 ⇒ K d V d T = 3 T 2 ⇒ d V = 3 T 2 K d T ⇒ γ V = 3 T 2 K as   d V = γ V d T ⇒ γ = 3 T 2 K V = 3 T 2 T 3 = 3 T